It's easy, I started off skiing, which is dead easy to master (The Art of the Snow Plough!) in a week, the course of your average holiday.
But for me snowboarding (to really enjoy it) took about 3 weeks, before that I was just cr*pping my pants about either:
a) Breaking my coccyx (sp?)
Knocking out my teeth!
It all depends on how accessible the slopes are, and like most Brits up until I spent a season scrubbing rich peoples bathrooms etc and serving them their food! I'd only ever spent a 'week-at-a-time' in the mountains.